The Hammers had a bid accepted for the 24-year-old Frenchman last week, but Vasiljevic has confirmed that the Premier League side pulled out at the final minute, despite terms being agreed.
"Osasuna received an offer from West Ham for Loe and we reached an agreement, which was just pending on the player passing his medical. Prior to his trip to London with his representative, we had already agreed everything between Osasuna and West Ham via email," he told reporters at a press conference.
"Loe travelled on Friday, because on the Saturday he would pass his medical. Then on Saturday, they started delaying the medical tests in London, while in Pamplona we received an email in which they told us the matter with Loe was now closed, because they had opted for another player instead, saying sorry and that's all."
Loe is widely regarded as one of the best midfielders in La Liga.